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Search: id:A094414
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| A094414 |
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Triangle T read by rows: dot product <1,2,...,r> * <s+1,s+2,...,r,1,2,...,s>. |
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11
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| 1, 5, 4, 14, 11, 11, 30, 24, 22, 24, 55, 45, 40, 40, 45, 91, 76, 67, 64, 67, 76, 140, 119, 105, 98, 98, 105, 119, 204, 176, 156, 144, 140, 144, 156, 176, 285, 249, 222, 204, 195, 195, 204, 222, 249, 385, 340, 305, 280, 265, 260, 265, 280, 305, 340, 506, 451
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Offset for r (the rows) is 1, for s (the columns) it is 0.
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FORMULA
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T(r, s) = r(2r^2 + 3r - 3rs + 1 + 3s^2)/6, r>=1, 0<=s<=r-1.
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EXAMPLE
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1
5 4
14 11 11
30 24 22 24
55 45 40 40 45
91 76 67 64 67 76
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MAPLE
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T:=proc(r, s) if s>=r then 0 else r*(2*r^2+3*r+1-3*r*s+3*s^2)/6 fi end: for r from 1 to 11 do seq(T(r, s), s=0..r-1) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 27 2006
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CROSSREFS
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Columns 0-6 are A000330, A006527, A026037, A026040, A026043, A026046, A026049. Row sums are A000537. See also A094415, A088003.
Sequence in context: A019068 A147685 A078930 this_sequence A158867 A107984 A133178
Adjacent sequences: A094411 A094412 A094413 this_sequence A094415 A094416 A094417
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, May 02 2004
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